Events & Seminars

2020 Jan 15

Analysis Seminar Dvoretsky Lecture: Sylvia Serfaty (NYU Courant) - Mean Field Limits for Coulomb Dynamics

12:00pm to 1:00pm

Location: 

Ross 70
We consider a system of N points evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow. By Riesz interaction, we mean inverse power s of the distance with s between d-2 and d where d denotes the dimension. We show a convergence result as N tends to infinity to the expected limiting evolution equation. This was previously an open question in general dimension, rendered difficult by the singular nature of the interaction. We will also discuss briefly similar results in the context of models of superfluidity and superconductivity.
2020 Jan 16

Dvoretzky Lectures: Systems of points with Coulomb interactions

Lecturer: 

Sylvia Serfaty
2:30pm to 4:30pm

Location: 

Manchester House, Lecture Hall 2
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability.We will first review these motivations, then present the ''mean-field'' derivation of effective models and equations describing the system at the macroscopic scale.
2020 Jan 15

Dvoretzky Lectures: Mean Field Limits for Coulomb Dynamics

Lecturer: 

Sylvia Serfaty
12:00pm to 2:00pm

Location: 

Ross 70
We consider a system of N points evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow. By Riesz interaction, we mean inverse power s of the distance with s between d-2 and d where d denotes the dimension. We show a convergence result as N tends to infinity to the expected limiting evolution equation.  This was previously an open question in general dimension, rendered difficult by the singular nature of the interaction. We will also discuss briefly similar results in the context of models of superfluidity and superconductivity.
2019 Nov 20

Logic Seminar - Christian d'Elbée

11:00am to 1:00pm

Location: 

Ross building - Room 63

Christian d'Elbée will speak about generic generic abelian varieties.

Generic generic abelian varieties.

Abstract: 
I will present work in progress in a new NSOP1 nonsimple theory: the expansion of an abelian variety by a generic subgroup, under some conditions on the endomorphism ring.  
2019 Dec 02

NT Seminar - Uriya First

2:30pm to 3:30pm

Location: 

Ross 70

Title: The Grothendieck--Serre conjecture for classical groups in low dimensions
Abstract:
A famous conjecture of Grothendieck and Serre predicts that if G is a reductive group scheme over a semilocal regular domain R and X is a G-torsor, then X has a point over the fraction field of R if and only if it has an R-point. Many instances of the conjecture have been established over the years. Most notably, Panin and Fedorov--Panin proved the conjecture when R contains a field.
2019 Nov 14

Basic Notions: Jake Solomon "Enumerative geometry over an arbitrary field"

4:00pm to 5:30pm

Location: 

Ross 70
Counting problems in algebraic geometry over an algebraically closed field have been studied for centuries. More recently, it was discovered that there are interesting counting problems over the real numbers. Topology took the place of algebraic closedness. However, the question remained whether there are interesting counting problems over more general fields where the tools of classical topology are not available. I will describe some results in this direction.
2019 Nov 28

Basic Notions: Eran Nevo (HUJI) "Algebraic Combinatorics a la Stanley".

4:00pm to 5:15pm

Location: 

Ross 70

The basic idea is to associate with a combinatorial object Xan algebraic structure A(X), and derive from algebraic properties of A(X)combinatorial consequences for X. For example, Stanley's proof of the UpperBound Theorem for simplicial spheres uses the Cohen-Macaulay property of theface ring associated with a simplicial complex.

We will review the basics of Stanley's theory, illustrate themon examples, and time permitting, discuss more recent advances of this theory.

(All needed terms and background will be given in thetalk.)   

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